Mourinho, who signed Cole from Arsenal in 2006, said there was still plenty more to come from the Stamford Bridge left-back.
"The brain controls, but the body needs to answer to the brain," said the Real Madrid boss. "His brain gives him, for sure, four to five years at a high level. I hope his body says yes.
"Ash is one of the best left-backs in the world. He is the kind of player who it is difficult to choose his best performance, because he is always so stable.
"I left England in 2007. At that time he was the best. Six years later he is still the best. He has won everything at club level and is getting his 100th cap. I believe the football world in England knows who he is."